An object and a screen are fixed on the uprights of an optical bench. The distance between them is $100 \, cm$. $A$ convex lens is placed in between the object and the screen and the position of the lens is so adjusted that the image of the object is formed on the screen at two conjugate positions of the lens. The distance between these conjugate positions of the lens is $40 \, cm$. What is the focal length of the lens in $cm$?
- A$15$
- B$18$
- C$21$
- D$24$
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